Unit 4 sec 2.2 Discrete and continuous

Unit 4 sec 2.2 Discrete and continuous

21 November 2015

14:41

  The distinction between discrete and continuous measures is important as it provides useful information about the nature of the data collected. As an introduction to these terms. Here is a contact that should help you get a sense of how they are used.

 The path itself is continuous, so precision on the path is possible, whereas the stepping stones placed on the path are discreet: they represent distinct, separate position with nothing in between any 2 consecutive steps. Using the path, you might mark your journey in terms of measured distance, whereas taking the same journey on the stepping stones involve counting out steps. In general, the distinction between measuring and counting is a useful way of identifying which majors are discreet and which are continuous.

  When it comes to statistical data, the same distinction can be made., foot length, on the other hand, has no such restriction - it is something that is measured on a continuous scale of measures and therefore produces continuous data.

One of the clearest distinctions between the numbers in the columns is that in some columns, the numbers seem to be discrete values well in other columns, the numbers seem to come from a continuous scale. Discrete data are data that can take one of a particular set of values: such data. Typically, though not necessarily, take integer values.

Here are some examples of discrete data

ª    the number of days in a week, on which one takes exercise.

ª    Number of × a particular website is visited in one day.

ª    The quality of a person’s recovery after a serious accident when called it 0 for full recovery, 1 for partial recovery and 2 for failure to recover.

Sometimes, as in the 3^rd example, discrete data arrays as a convenient way of recording data whose outcome is really some non-numerical category. A widely occurring example of this is when there are just 2 numerical values, and said to be binary data

why discrete data, continuous data can take all the in between values on the number scale. In theory, and depending on the context, they may take any numerical value from the set of real numbers, either negative or positive. Alternatively, they may be constrained to be positive or they may be limited it to a finite interval. Notice that all these columns contain data that take positive values.

Mass and weight

did you notice that the weights in table 2 given in kilograms, even though the kilogram is a unit of mass?

 The mass of an object is a major of the amount of matter that it contains, whereas its weight is a major of the gravitational force acting on it. Weight, being force is measured in newtons. However, you will often seem weights quoted in kilograms in everyday life, and this informal approach will sometimes be used in MU123 too.

You were deliberately not told in this activity. What level of precision to use? You might have written down 21cm and this would have carried the implication that the page width was nearer 21cm than 20cm or 22cm. again, they would be an implication that the actual measurements were nearer 211mm than 212mm. if you had access to more precise measuring device still, you might have been able to write down 211.0mm or 211.03mm, and so.

However, no matter how good you measuring device, you would never be able to say what the exact width of the particular sheet of paper was.

  The edge of a piece of paper is by no means straight and smooth - in that, the closer we work, the rougher the age be used to be. Clearly there is a limit to the precision with which is in meaningful to describe it width. However, the law particular purposes, there is no need for extreme precision, and recording the value of the width correct to, say, the nearest centimetre or the nearest millimetre may well suffice.

  In practice, for all manufactured items. There is a tolerance for the possible range of sizes that each item can be. According to the ISO standard, the width of manufactured A4 paper should be 210 ± 2mm. this is despite the mathematical exactness suggested in unit 3 of how ISO paper size relate to each other.

  There is a sense in which each of the columns C to H in table 2 can be considered to contain continuous data. It is just that the measurement and recording process has resulted in these columns of data being presented correct to the nearest month, year, centimetre, tenth of a kilogram, and hundredth of a kilogram, respectively.

 It follows that while the actual values of 2 items of continuous data can never strictly be identical, then started well use, into a contain degree of precision, may well be.

 You will not be right to think that all major dictator are actually discrete, but the idea of continuous data remains useful both contractually and when creating mathematical and statistical models of the world